Cylinder Volume Calculator
Cylinder volume calculator: volume, curved and total surface area, litres and gallons from radius or diameter and height. Hollow option included.
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How the Cylinder Volume Calculator Formula Works
A cylinder is a circle stretched straight up. Its volume is the area of the circular base times the height. The base area is pi times the radius squared, so V = pi r2 h. If you only know the diameter, halve it first. A radius of 6 cm and a height of 12 cm give 1,357.17 cubic centimetres.
The surface has three parts: the curved side and two flat circles. Unrolled, the side is a rectangle as tall as the cylinder and as wide as the circle's circumference, so the curved surface area, CSA, is 2 pi r h. Adding the two ends, each pi r2, gives the total surface area, TSA = 2 pi r (r + h).
To turn volume into something you can buy or pour, the calculator converts to litres, US gallons, imperial gallons, cubic feet, cubic metres and cubic inches. A fill percentage scales the liquid for an upright cylinder that is only partly full. For a pipe or tube, the hollow option subtracts the inner cylinder and also reports the space inside.
V = pi × r2 × h; CSA = 2 × pi × r × h; TSA = 2 × pi × r × (r + h); hollow: V = pi × h × (R2 − r2)- rlengthRadius of the circular base, half the diameter.
- hlengthHeight of the cylinder, the distance between the two bases.
- R, r (hollow)lengthOuter and inner radius of a hollow cylinder.
- Vlength cubedVolume; for a hollow cylinder, the wall material.
- fill%How full the inside is, for liquid capacity.
- r
- length
- Radius of the circular base, half the diameter.
- h
- length
- Height of the cylinder, the distance between the two bases.
- R, r (hollow)
- length
- Outer and inner radius of a hollow cylinder.
- V
- length cubed
- Volume; for a hollow cylinder, the wall material.
- fill
- %
- How full the inside is, for liquid capacity.
Using the Cylinder Volume Calculator
Enter length unit
Choose from Millimetres, Centimetres, Metres, Inches, Feet, Yards.
Enter i know the
Choose from Radius, Diameter.
Enter radius or diameter (outer, in your unit)
Type the figure you already have, then press Calculate.
Enter height or length (in your unit)
Type the figure you already have, then press Calculate.
Enter cylinder type
Choose from Solid or filled (one radius), Hollow (pipe or tube, two radii).
Enter inner radius or diameter (in your unit)
Type the figure you already have, then press Calculate.
Enter how full for liquid (%)
Any value between 0 and 100.
Read the result
Press Calculate to update the result. Until you do, the last result is dimmed and marked as out of date, so you always know which numbers belong to the values in the boxes.
A Real Worked Example
A cylinder has a radius of 6 cm and a height of 12 cm. The base area is pi x 62 = 113.097 square cm, so the volume is 113.097 × 12 = 1,357.168 cubic cm.
The curved surface area is 2 pi x 6 × 12 = 452.389 square cm and the total surface area is 678.584. Filled with liquid it holds 1.357 litres, which is 0.359 US gallons.
A 4 x 8 inch cylinder, by diameter
Choose inches and the diameter option, with 4 across and 8 tall. The radius is 2 inches, so the volume is pi x 4 × 8 = 100.531 cubic inches.
That is 1.647 litres or 0.435 US gallons, and 0.0582 cubic feet. The total surface area is 125.664 square inches.
A 6 ft x 8 ft water tank, 75 percent full
Choose feet and diameter, 6 across and 8 tall, with the fill set to 75 percent. The full volume is pi x 32 × 8 = 226.19 cubic feet.
At 75 percent the liquid is 169.65 cubic feet, 1,269.0 US gallons or 4,804 litres. A full tank holds 1,692.1 US gallons.
A hollow concrete tube, 12 in outside and 10 in inside, 36 in long
Choose the hollow option in inches with an outer diameter of 12, an inner diameter of 10 and a length of 36. The wall material is pi x 36 × (36 − 25) = 1,244.07 cubic inches.
The space inside is pi x 25 × 36 = 2,827.43 cubic inches, which holds 12.24 US gallons. The surface area counts the outer wall, the inner wall and both ring-shaped ends.
A 1.2 m x 1.5 m cylinder in metres
Choose metres and diameter, 1.2 across and 1.5 tall. The radius is 0.6 m, so the volume is pi x 0.36 × 1.5 = 1.696 cubic metres.
That is 1,696.5 litres, 448.2 US gallons or 373.2 imperial gallons.
A small 25 mm radius, 100 mm cylinder
Choose millimetres with a radius of 25 and a height of 100. The volume is pi x 625 × 100 = 196,349.5 cubic millimetres.
That is 0.196 litres, or 196.3 millilitres. For small sizes the calculator shows three decimals so these values stay readable.
What Else to Know
How the Cylinder Volume Formula Works
The volume of a cylinder is the area of its circular base multiplied by its height. The base area is pi times the radius squared, so V = pi r2 h. Because the radius is squared, a small change in it matters more than the same change in height.
If you know the diameter instead, halve it to get the radius, or switch the calculator to the diameter option and it does that for you. Use one length unit for both the radius and the height. The result is in cubic units of that length unit, with litres and gallons alongside.
The standard formulas for a right circular cylinder are listed on the Wikipedia page for Cylinder, which this calculator follows.
Volume, Lateral Surface Area and Total Surface Area
Three numbers describe a cylinder: volume, CSA and TSA. Volume is the space inside. CSA, the curved or lateral surface area, is the side wall alone and equals 2 pi r h. TSA, the total surface area, adds the two circular ends, each pi r2, giving 2 pi r (r + h).
Use CSA when you only cover the side, such as wrapping a label round a can or painting a pipe. Use TSA when you cover every face. For a cup open at the top, use the curved area plus one base.
The surface area table lists CSA and TSA for several sizes.
Cylinder Volume in Litres and Gallons
Litres and gallons answer a practical question: how much liquid fits? The calculator converts the volume from cubic units to litres with the exact definitions of the units. A litre is 1,000 cubic centimetres, a US gallon is exactly 231 cubic inches or 3.785411784 litres, and an imperial gallon is 4.54609 litres.
The fill percentage scales the liquid for an upright cylinder, because the liquid is itself a cylinder of lower height. The capacity table shows common diameters and heights in inches with litres and both gallons.
This page is the pure geometry of a cylinder. A horizontal tank part full, a capsule or a sphere needs a different calculation, which a tank volume tool handles.
Hollow Cylinder Volume for Pipes and Tubes
A hollow cylinder, such as a pipe, a tube or a concrete ring, has an outer radius R and an inner radius r. Its wall material is the outer cylinder minus the inner one: V = pi h (R2 − r2). Its inside volume, which holds liquid, is pi r2 h.
Choose the hollow option and give the outer and inner sizes. The headline volume is then the wall material, and the capacity outputs use the inside. The surface area includes the outside wall, the inside wall and the two ring-shaped ends.
The inner size must be smaller than the outer size.
Metric and Imperial Units
Pick millimetres, centimetres, metres, inches, feet or yards. Volume scales with the cube of the length factor, so one metre is 100 cm but one cubic metre is 1,000,000 cubic cm. That is why you should convert lengths first, not the finished volume by the length factor.
For metric work, enter centimetres and read litres directly: 1,000 cubic cm is 1 litre. For US work, enter inches and divide cubic inches by 231 for gallons, or read the US gallon output.
Unit definitions follow the Wikipedia pages for the cubic foot and the gallon.
Worked Cylinder Examples
The radius 6 cm, height 12 cm example gives 1,357.168 cubic cm, which is 1.357 litres. The 4 × 8 inch example gives 100.531 cubic inches, or 0.435 US gallons. The tank, hollow tube, metre and millimetre examples cover the other modes.
Doubling the radius quadruples the volume, while doubling the height only doubles it. The scaling table shows this with real numbers.
Try your own values in the calculator and compare with these examples to check your inputs.
Limits and Related Calculators
The calculator treats a perfect right circular cylinder with flat ends. It does not include rounded or conical tank ends, wall thickness for a tank unless you use the hollow option, or a part-full horizontal cylinder. Real vessels also have fittings and a usable capacity lower than the geometric one.
For materials that fill a round hole or form, see the gravel calculator and the stone calculator. To find a fill share, the percentage calculator helps. For a rough check of cubic units, the river rock calculator uses the same volume ideas.
Reference Tables
| Quantity | Solid cylinder | Hollow cylinder |
|---|---|---|
| Volume | V = pi r2 h | V = pi h (R2 − r2) |
| Base area | pi r2 | pi (R2 − r2) |
| Lateral (curved) surface area, CSA | 2 pi r h | 2 pi (R + r) h |
| Total surface area, TSA | 2 pi r (r + h) | CSA + 2 pi (R2 − r2) |
| Circumference of the base | 2 pi r | 2 pi R (outer) |
| Capacity (inside volume) | pi r2 h | pi r2 h with the inner radius |
| Radius (cm) | Height 5 cm | Height 10 cm | Height 12 cm | Height 20 cm | Height 50 cm |
|---|---|---|---|---|---|
| 2 | 62.8 | 125.7 | 150.8 | 251.3 | 628.3 |
| 3 | 141.4 | 282.7 | 339.3 | 565.5 | 1,413.7 |
| 4 | 251.3 | 502.7 | 603.2 | 1,005.3 | 2,513.3 |
| 5 | 392.7 | 785.4 | 942.5 | 1,570.8 | 3,927.0 |
| 6 | 565.5 | 1,131.0 | 1,357.2 | 2,261.9 | 5,654.9 |
| 8 | 1,005.3 | 2,010.6 | 2,412.7 | 4,021.2 | 10,053.1 |
| 10 | 1,570.8 | 3,141.6 | 3,769.9 | 6,283.2 | 15,708.0 |
| Radius (cm) | Height (cm) | Base area | Lateral area (CSA) | Total area (TSA) |
|---|---|---|---|---|
| 3 | 10 | 28.3 | 188.5 | 245.0 |
| 5 | 10 | 78.5 | 314.2 | 471.2 |
| 6 | 12 | 113.1 | 452.4 | 678.6 |
| 8 | 20 | 201.1 | 1,005.3 | 1,407.4 |
| 10 | 25 | 314.2 | 1,570.8 | 2,199.1 |
| 15 | 40 | 706.9 | 3,769.9 | 5,183.6 |
| Diameter (in) | Height (in) | Litres | US gallons | Imperial gallons |
|---|---|---|---|---|
| 4 | 8 | 1.65 | 0.44 | 0.36 |
| 6 | 12 | 5.56 | 1.47 | 1.22 |
| 8 | 24 | 19.77 | 5.22 | 4.35 |
| 12 | 24 | 44.48 | 11.75 | 9.78 |
| 18 | 36 | 150.12 | 39.66 | 33.02 |
| 24 | 36 | 266.88 | 70.50 | 58.71 |
| 24 | 48 | 355.84 | 94.00 | 78.27 |
| 36 | 48 | 800.64 | 211.51 | 176.12 |
| Fill | Liquid height (cm) | Litres | US gallons | Cubic inches |
|---|---|---|---|---|
| 10% | 1.2 | 0.136 | 0.036 | 8.28 |
| 25% | 3.0 | 0.339 | 0.090 | 20.70 |
| 50% | 6.0 | 0.679 | 0.179 | 41.41 |
| 75% | 9.0 | 1.018 | 0.269 | 62.11 |
| 90% | 10.8 | 1.221 | 0.323 | 74.54 |
| 100% | 12.0 | 1.357 | 0.359 | 82.82 |
| Outer dia. (in) | Inner dia. (in) | Wall (in) | Wall volume (cu in) | Capacity (US gal) |
|---|---|---|---|---|
| 4 | 3.5 | 0.250 | 106.0 | 1.50 |
| 6 | 5.5 | 0.250 | 162.6 | 3.70 |
| 8 | 7.25 | 0.375 | 323.4 | 6.43 |
| 12 | 10 | 1.000 | 1,244.1 | 12.24 |
| 12 | 11 | 0.500 | 650.3 | 14.81 |
| 24 | 22 | 1.000 | 2,601.2 | 59.24 |
| 24 | 20 | 2.000 | 4,976.3 | 48.96 |
| Change | Radius | Height | Volume | Volume ratio | Total area |
|---|---|---|---|---|---|
| Start | 6.00 | 12.00 | 1,357.2 | 1.00 x | 678.6 |
| Double the radius | 12.00 | 12.00 | 5,428.7 | 4.00 x | 1,809.6 |
| Double the height | 6.00 | 24.00 | 2,714.3 | 2.00 x | 1,131.0 |
| Double both | 12.00 | 24.00 | 10,857.3 | 8.00 x | 2,714.3 |
| Half the radius | 3.00 | 12.00 | 339.3 | 0.25 x | 282.7 |
| Half the height | 6.00 | 6.00 | 678.6 | 0.50 x | 452.4 |
| From | To | Multiply by |
|---|---|---|
| Cubic centimetres | Litres | 0.001 |
| Cubic metres | Litres | 1,000 |
| Cubic inches | Cubic centimetres | 16.387064 |
| Cubic feet | Litres | 28.316847 |
| US gallons | Litres | 3.785412 |
| Imperial gallons | Litres | 4.54609 |
| Cubic feet | US gallons | 7.480520 |
| Cubic yards | Cubic feet | 27 |
| Term | Meaning |
|---|---|
| Radius | Distance from the centre of the circular base to its edge, half the diameter |
| Diameter | Width of the circular base through its centre, twice the radius |
| Height | Distance between the two circular bases, also called length for a horizontal cylinder |
| CSA | Curved or lateral surface area: the side wall without the two ends |
| TSA | Total surface area: the side wall plus both ends |
| Capacity | How much liquid the inside holds, found from the inner dimensions |
| Hollow cylinder | A cylinder with a cylindrical hole through it, such as a pipe or a tube |
| Mistake | Effect | Fix |
|---|---|---|
| Using the diameter as the radius | Volume is four times too large | Halve the diameter, or choose diameter in the calculator |
| Mixing units, such as inches and feet | Wrong by a factor of 12 or more | Convert first, or pick one unit for both |
| Cubing the wrong conversion | Litres or gallons are off | Volume converts by the cube of the length factor |
| Using the outer size for capacity | Capacity is too high | Use the inner diameter for what the vessel holds |
| Forgetting the ends in surface area | TSA too small | Add 2 pi r2 to the lateral area |
| Using US gallons for an imperial gallon source | About 20 percent out | Check which gallon the label means |
Frequently Asked Questions About the Cylinder Volume Calculator
How do you calculate cylindrical volume?
Multiply the area of the circular base by the height. The base area is pi times the radius squared, so V = pi r2 h. With a radius of 6 cm and a height of 12 cm, the base area is 113.10 square cm and the volume is 1,357.17 cubic cm. Use consistent units for every length. Enter your own radius or diameter and height in the calculator for an exact answer.
What is CSA, TSA and volume of a cylinder?
CSA is the curved surface area, 2 pi r h, the side wall alone. TSA is the total surface area, 2 pi r (r + h), which adds both circular ends. Volume is pi r2 h. For r = 6 and h = 12 these are 452.39, 678.58 and 1,357.17. Enter your own radius or diameter and height in the calculator for an exact answer.
What is the volume of a 4x8 cylinder?
A 4 × 8 cylinder usually means 4 units across and 8 units tall. The radius is 2, so V = pi x 22 × 8 = 100.53 cubic units. In inches that is 100.53 cubic inches, 1.647 litres or 0.435 US gallons. If 4 is the radius instead, the volume is 402.12. Enter your own radius or diameter and height in the calculator for an exact answer.
Volume of a cylinder with radius 6cm and height 12cm?
V = pi x 62 × 12 = 432 pi = 1,357.17 cubic centimetres. That is 1.357 litres, because 1,000 cubic centimetres make a litre, or 0.359 US gallons. The curved area is 452.39 square cm and the total surface area is 678.58. Enter your own radius or diameter and height in the calculator for an exact answer.
What is the cylindrical volume calculator formula?
The formula is V = pi r2 h, where r is the base radius and h is the height. If you know the diameter d, use V = pi d2 h / 4. Surface area uses CSA = 2 pi r h and TSA = 2 pi r (r + h). For a hollow cylinder, subtract the inner cylinder: V = pi h (R2 − r2). Enter your own radius or diameter and height in the calculator for an exact answer.
How do I find cylinder volume in litres?
Work in centimetres, then divide cubic centimetres by 1,000, or work in metres and multiply cubic metres by 1,000. A cylinder 30 cm across and 50 cm tall holds 35,342.9 cubic cm, which is 35.34 litres. The calculator converts from any length unit. Enter your own radius or diameter and height in the calculator for an exact answer.
How do I calculate cylinder volume in metric?
Enter the radius or diameter and the height in millimetres, centimetres or metres. The volume is in cubic units of the same length unit, and the calculator also gives litres and cubic metres. A cylinder 1.2 m across and 1.5 m tall is 1.696 cubic metres, or 1,696 litres. Enter your own radius or diameter and height in the calculator for an exact answer.
How do I find volume from the diameter?
Halve the diameter to get the radius, then use V = pi r2 h. Or use V = pi d2 h / 4 directly. A cylinder 10 inches across and 20 inches tall has volume 1,570.8 cubic inches, the same as radius 5: 1,570.8. Pick the diameter option in the calculator to skip the halving. Enter your own radius or diameter and height in the calculator for an exact answer.
How do I find the height from the volume?
Rearrange the formula to h = V / (pi r2). If a cylinder of radius 5 cm holds 1,000 cubic cm, the height is 1000 / (78.540) = 12.73 cm. Likewise r = √(V / (pi h)) when the height is known. Enter your own radius or diameter and height in the calculator for an exact answer.
What is the volume of a hollow cylinder?
Subtract the inner cylinder from the outer one: V = pi h (R2 − r2). A pipe with outer radius 5 cm, inner radius 4 cm and length 20 cm holds 565.49 cubic cm of material and 1,005.31 cubic cm inside. Choose the hollow option and enter both sizes. Enter your own radius or diameter and height in the calculator for an exact answer.
How many gallons are in a cylinder?
Find the volume in cubic inches and divide by 231, since a US gallon is exactly 231 cubic inches. A cylinder 12 in across and 24 in tall is 2,714.3 cubic inches, which is 11.75 US gallons. Divide litres by 3.785412 for the same result. Enter your own radius or diameter and height in the calculator for an exact answer.
What is the difference between US and imperial gallons?
A US gallon is 3.785412 litres and an imperial gallon is 4.54609 litres, so the imperial one is about 20 percent bigger. The same cylinder, 6 cm radius and 12 cm tall, holds 0.359 US gallons or 0.299 imperial gallons. The calculator shows both. Enter your own radius or diameter and height in the calculator for an exact answer.
How do I find the surface area of an open cylinder?
An open-top cup or bucket has one base. Add the curved area and one base: pi r2 + 2 pi r h. For r = 6 and h = 12 that is 113.1 + 452.4 = 565.5 square cm. A tube open at both ends has only the curved area. Enter your own radius or diameter and height in the calculator for an exact answer.
What happens to volume if the radius doubles?
Volume grows with the square of the radius, so doubling the radius makes the volume four times larger. Doubling the height only doubles it. From r = 6 and h = 12, radius 12 gives 5,428.7 against 1,357.2, a ratio of 4.0. Enter your own radius or diameter and height in the calculator for an exact answer.
How do I convert cylinder volume to cubic feet?
Convert the lengths to feet first, or convert the volume with 1 cubic foot = 1,728 cubic inches. A cylinder 24 in across and 36 in tall is 16,286.0 cubic inches, which is 9.425 cubic feet. The calculator gives cubic feet for any input unit. Enter your own radius or diameter and height in the calculator for an exact answer.
How much liquid is in a partly filled cylinder?
For an upright cylinder, the liquid is also a cylinder, so multiply by the fill fraction. Set the fill percentage in the calculator. A 6 cm radius, 12 cm tall cylinder filled to 75 percent holds 1.018 litres. A cylinder lying on its side needs a different formula. Enter your own radius or diameter and height in the calculator for an exact answer.
When should I use a tank calculator instead?
Use this page for the pure geometry of an upright or standalone cylinder. A horizontal tank filled part way, a capsule or a sphere needs formulas for a circular segment or a spherical cap, which this calculator does not apply. Choose a tank volume tool for those shapes and a fill depth. Enter your own radius or diameter and height in the calculator for an exact answer.
Does the formula work for a slanted cylinder?
Yes, if you use the perpendicular height, the distance between the two base planes, not the slanted side length. The volume of an oblique cylinder equals the base area times that perpendicular height. The curved surface area does change, so the surface outputs are for a right cylinder. Enter your own radius or diameter and height in the calculator for an exact answer.
How do I find the volume of half a cylinder?
Calculate the full cylinder and halve it. A half cylinder of radius 6 cm and length 12 cm has volume 678.58 cubic cm. Its surface area is not simply half, since the flat cut face is new: add 2 r h for that rectangle. Enter your own radius or diameter and height in the calculator for an exact answer.
How much does the water in a cylinder weigh?
Fresh water is about 1 kilogram per litre, 1,000 kilograms per cubic metre. A full cylinder of 6 cm radius and 12 cm height holds 1.357 litres, about 1.36 kg. In US units a gallon of water is about 8.34 pounds. Enter your own radius or diameter and height in the calculator for an exact answer.
Why are my litres different from another tool?
The usual causes are using the diameter as the radius, using the outer size of a vessel instead of the inner size, or mixing US and imperial gallons. Check the units and the radius or diameter option first. Wall thickness, rounded ends and cone bottoms also change real tank capacity. Enter your own radius or diameter and height in the calculator for an exact answer.
How accurate is the cylinder volume calculator?
The arithmetic is exact for a perfect right circular cylinder. Real objects are rarely perfect, and a measuring error is squared when it is in the radius. A 2 percent error in the radius gives about a 4 percent error in volume, so measure the radius carefully. Enter your own radius or diameter and height in the calculator for an exact answer.
References
- [1] Wikipedia contributors. “Cylinder.” Wikipedia. Accessed 2026-10-07.
- [2] Wikipedia contributors. “Cubic foot.” Wikipedia. Accessed 2026-10-07.
- [3] Wikipedia contributors. “Gallon.” Wikipedia. Accessed 2026-10-07.
- [4] Wikipedia contributors. “Annulus (mathematics).” Wikipedia. Accessed 2026-10-07.
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